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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Probing the interface structure of block copolymer compatibilizers in semicrystalline polymer blends

Abstract The use of block copolymers to compatibilize immiscible plastics is an important strategy for upcycling municipal plastic wastes. Multiblock copolymers (MBCPs) have been proven to be more effective compatibilizers than di‐ and tri‐block copolymers. Herein, we probe the interface structure of an effective multiblock copolymer compatibilizer and compare that with an ineffective triblock copolymer (TBCP). The interface activity of the compatibilizers is understood through a combination of small‐angle neutron and x‐ray scatterings (SANS and SAXS), by using deuterated homopolymer matrix and protonated compatibilizers. SANS analysis suggests that the MBCP forms a thicker interface layer (7–9 nm) than the TBCP (0–4 nm). In addition, SANS data seems to point to a stronger tendency for the MBCP to locate at the interface. Both factors contribute to its effectiveness at compatibilizing immiscible homopolymers.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Determination of the Structures of Lignin Subunits and Nanoparticles in Solution by Small‐Angle Neutron Scattering: Towards Improving Lignin Valorization

Abstract Lignin nanoparticles (LNPs) are usually produced from lignin solution through supersaturation. The structure of the lignin in solution is still poorly understood due to structural variability of isolated lignins. Here, lignins were extracted from different plants to establish a general pattern of their structure in several lignin solvents. Lignin molecules (lignin subunits) and larger aggregates were observed in dimethyl sulfoxide (DMSO), ethylene glycol (EG) and 0.1 N NaOD solutions by small‐angle neutron scattering (SANS). It was proposed that the aggregates were composed of lignin subunits with a higher molecular weight and a higher ratio of the aliphatic to phenolic hydroxyl groups. The size, shape, and compactness are important factors that affect the uses of the LNPs, which were obtained from the SANS data for the first time. A discrepancy in the radius between SANS and DLS was discovered, pointing to a large hydration shell around the LNPs in aqueous solutions. The cytotoxicity of the corncob lignin, kraft lignin, and their LNPs were measured and compared.

Zhang, Xin↗
DOE OSTI2021

Incorporation of Membrane Proteins Into Bicontinuous Microemulsions Through Winsor‐III System‐Based Extraction

Abstract The membrane proteins (MP) α‐synuclein (ASYN) and bacteriorhodopsin (BR) were readily incorporated into bicontinuous microemulsions (BμEs) formed by two microemulsion systems: water/heptane/Aerosol‐OT (AOT)/CK‐2,13 and water/dodecane/sodium dodecyl sulfate (SDS)/1‐pentanol. (CK‐2,13 is an alkyl ethoxylate possessing two alkyl tail groups of carbon chain length 2 and 13 and an average degree of ethoxylation of 5.6.) MP were encapsulated in BμEs through preparation of Winsor‐III systems at optimal salinity, with the anionic surfactants AOT and SDS providing the driving force for extraction. Dissolution of ASYN in BμEs greatly increased the former's α‐helicity, similar to ASYN's behavior in the presence of biomembranes, while BμE‐ and vesicle‐encapsulated BR possessed similar secondary structure. Small‐angle neutron scattering (SANS) results clearly demonstrated the direct interaction of MP with the surfactants, resulting in a decrease of surface area per volume for surfactant monolayers due to decreased surfactant efficiency. The SANS signal for ASYN was isolated through the use of neutron contrast matching for the surfactants through partial deuteration of water and oil, one of the first reports of contrast matching for BμEs in the literature. The SANS results of the contrast‐matched sample reflected similar aggregation for ASYN in BμEs as was reported previously for vesicles and SDS solution. This study demonstrates the potential use of BμEs as MP host systems for conducting biochemical reactions such as the conversion of sunlight into adenosine triphosphate by BR and studying the fundamental behavior of MP, such as the role of ASYN dysfunction in Parkinson's disease, as well as for isolation and purification of MP via Winsor‐III‐based extraction.

Hayes, Douglas G.↗
DOE OSTI2020

Cell fusing agent virus (Flavivirus) infection in Aedes aegypti in Texas: seasonality, comparison by trap type, and individual viral loads

Abstract South Texas has experienced local transmission of Zika virus and of other mosquito-borne viruses such as chikungunya virus and dengue virus in the last decades. Using a mosquito surveillance program in the Lower Rio Grande Valley (LRGV) and San Antonio, TX, from 2016 to 2018, we detected the presence of an insect-specific virus, cell fusing agent virus (CFAV), in the Aedes aegypti mosquito population. We tested 6,326 females and 1,249 males from the LRGV and 659 females from San Antonio for CFAV by RT-PCR using specific primers. Infection rates varied from 0 to 261 per 1,000 mosquitoes in the LRGV and 115 to 208 per 1,000 in San Antonio depending on the month of collection. Infection rates per 1,000 individuals appeared higher in females collected from BG Sentinel 2 traps compared to Autocidal Gravid Ovitraps, but the ratio of the percentage of infected pools did not differ by trap type. The natural viral load in individual males ranged from 1.25 x 10 2 to 5.50 x 10 6 RNA copies and in unfed females from 5.42 x 10 3 to 8.70 x 10 6 RNA copies. Gravid females were found to harbor fewer viral particles than males and unfed females.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Neutron scattering in photosynthesis research: recent advances and perspectives for testing crop plants

The photosynthetic performance of crop plants under a variety of environmental factors and stress conditions, at the fundamental level, depends largely on the organization and structural flexibility of thylakoid membranes. These highly organized membranes accommodate virtually all protein complexes and additional compounds carrying out the light reactions of photosynthesis. Most regulatory mechanisms fine-tuning the photosynthetic functions affect the organization of thylakoid membranes at different levels of the structural complexity. In order to monitor these reorganizations, non-invasive techniques are of special value. On the mesoscopic scale, small-angle neutron scattering (SANS) has been shown to deliver statistically and spatially averaged information on the periodic organization of the thylakoid membranes in vivo and/or, in isolated thylakoids, under physiologically relevant conditions, without fixation or staining. More importantly, SANS investigations have revealed rapid reversible reorganizations on the timescale of several seconds and minutes. In this paper, we give a short introduction into the basics of SANS technique, advantages and limitations, and briefly overview recent advances and potential applications of this technique in the physiology and biotechnology of crop plants. We also discuss future perspectives of neutron crystallography and different neutron scattering techniques, which are anticipated to become more accessible and of more use in photosynthesis research at new facilities with higher fluxes and innovative instrumentation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Porosity in nuclear graphite and its impact on nuclear reactor science and criticality safety applications

Porosity in nuclear-grade graphite significantly influences its low-energy neutron scattering, yet its effect on underlying phonon properties remains debated. Here, this work integrates inelastic and small-angle neutron scattering (INS/SANS) experiments, advanced atomistic simulations with a novel machine-learned potential (DeepMD), total cross-section measurements, and neutronics calculations (SCALE, MCNP, OpenMC) to investigate porosity’s impact on neutron thermalization. INS measurements on diverse graphite grades reveal no discernible porosity effect on phonon spectra, which align with crystalline graphite. Conversely, total cross-section data below ≈10 meV show increased scattering attributable to SANS. Our DeepMD simulations demonstrate that realistic micropores do not distort phonon spectra, challenging the assumptions in current ENDF/B-VIII.1 porosity thermal scattering laws (TSLs). These TSLs, based on random atom removal, produce unphysical phonon spectra and inflate inelastic cross-sections. Augmenting a crystalline TSL with an SANS component accurately captures experimental total cross-sections. Neutronics benchmarks (ICSBEP/IRPhE) show ENDF porosity TSLs unphysically increase neutron multiplication factor, keff. Crucially, incorporating SANS physics (NCrystal/OpenMC) indicates accurately modeled porosity negligibly affects keff, reactor physics, or criticality safety.

Critical benchmarks↗
DOE OSTI2021

Effect of stereochemistry on nanoscale assembly of ABA triblock copolymers with crystallizable blocks

We report on the nanoscale assembly of poly(lactic acid)-b-poly(ethylene oxide)-b-poly(lactic acid) (PLA-PEO-PLA) triblock copolymers in water, focusing on the effect of stereochemistry, where the PLA blocks are statistical copolymers of l-lactide and d-lactide with l/d ratios of 100/0, 95/5, 90/10, 85/15, 75/25, and 50/50. Small-angle neutron scattering (SANS) shows a nearly constant d-spacing as concentration varies in triblock systems with l/d ratios of 90/10 and 95/5, which we attribute to inhomogeneity in the structure of these gels, supported by previous USANS and confocal microscopy studies. The SANS data fit well to a core-shell ellipsoid form factor model with a hard-sphere structure factor. Polymeric micelles with l/d ratios from 75/25 to 85/15 displayed very high aggregation numbers, consistent with a strong interaction between PLA chains and the enhanced storage modulus observed in rheological studies of these systems. While the 90/10 and 95/5 samples showed lower aggregation numbers, their SANS profiles shows close spacing between micelles, which may promote a high fraction of intermicellar bridging chains, also consistent with a higher storage modulus. Overall, these results provide insight into the micellar assembly behavior of block copolymers with a crystallizable block, and indicate that tuning stereochemistry of PLA-based block copolymers is an effective means of modifying micellar properties for specific applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Probing the Core–Shell Organization of Nanoconfined Methane in Cylindrical Silica Pores Using In Situ Small-Angle Neutron Scattering and Molecular Dynamics Simulations

Determining the structure of nanoconfined fluids is essential for predicting the fate of these fluids in subsurface geologic formations with nanoporous features and for engineering novel nanoporous materials for storing compressed gases. In this study, we probe the structure of nanoconfined methane at pressures in the range of 15–100 bar using in situ small-angle neutron scattering (SANS) measurements and molecular dynamics (MD) simulations. The structure of methane is probed in MCM-41 and SBA-15 with cylindrical pores and diameters of 3.3 and 6.8 nm, respectively. In situ SANS measurements and MD simulations showed that the confined methane molecules are organized in a core–shell structure, with the shell arising from the adsorption of methane molecules on the silica surface. The shell thicknesses of the adsorbed deuterated methane (CD4) molecules in MCM-41 obtained by SANS measurements are 1.4 ± 0.5, 2.1 ± 0.1, 3.2 ± 0.8, 4.0 ± 0.3, and 6.0 ± 0.7 Å at equilibrated pressures of 15.6, 35.6, 55.5, 73.3, and 95.7 bar, respectively. The shell thicknesses of the adsorbed CD4 layer in SBA-15 pores are 2.7 ± 0.5, 4.3 ± 0.7, 6.6 ± 0.7, 10.2 ± 0.3, and 14.6 ± 0.8 Å at equilibrated pressures of 15.5, 32.7, 52.4, 70, and 99.5 bar, respectively. These experimental results are in close agreement with the results predicted from MD simulations. Adsorption of methane molecules on the silica surfaces is primarily driven by van der Waals interactions between the methane molecules and the hydroxyl groups on the silica surface, while electrostatic interactions play a minor role. In conclusion, the experimental and simulation approaches described in this study provide fundamental insights into the organization of confined gases using methane as a specific example in the context of compressed fluid storage in natural and engineered materials for adaptive energy use.

03 NATURAL GAS↗
DOE OSTI2021

Multiscale Structural Characterization of a Smectic Liquid Crystalline Elastomer upon Mechanical Deformation Using Neutron Scattering

Liquid crystalline elastomers (LCEs) exhibit unique shape memory behavior due to the combination of liquid crystalline orientation and rubber elasticity. Multiscale structural characterization of these materials upon deformation is crucial to understanding their structure–property relationships. In this work, the structure evolution of an epoxy-based, main-chain LCE with deuterated flexible spacers upon uniaxial mechanical deformation is investigated at different length scales. Wide-angle and small-angle X-ray scattering (WAXS/SAXS) reveal the presence of smectic polymorphism and rotations of the smectic domains upon mechanical stretching, which is also confirmed by small-angle neutron scattering (SANS). Importantly, the selective deuteration enables an improved neutron scattering contrast between the smectic and amorphous domains. SANS patterns of the deformed, deuterated LCE exhibit strong scattering streaks that are not observed in SAXS or SANS of hydrogenated LCE, indicating the presence of highly aligned amorphous domains. The macroscopic orientation also results in the formation of structures in the micrometer scale revealed by the ultrasmall-angle neutron scattering (USANS) experiment.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Signatures of Thermoreversible Associations in X-ray and Neutron Scattering from Dilute Polyzwitterion Solutions

In aqueous solutions of polyzwitterions (PZs), an interplay between dipole–dipole interactions and hydration of zwitterionic groups can lead to thermoreversible associations, which have been difficult to detect in experiments. Here, in this study, we investigated dilute aqueous solutions of poly(1-(3-sulphonatopropyl)-2-vinylpyridinium) (P2VPPS) using small-angle X-ray and neutron scattering (SAXS and SANS) to probe the structure and neutron spin-echo (NSE) spectroscopy to probe dynamics. The SAXS and SANS data show that the correlation length increases with an increase in the concentration of P2VPPS for three different molecular weights. The addition of 0.1 M NaCl to one of the solutions led to almost no dependence of the correlation length on the concentration. Such a concentration dependence of the correlation length suggests the formation of clusters driven by thermoreversible associations in the solutions. The NSE measurements show that the solutions with a larger correlation length display slower relaxation, reflecting the reduced mobility of larger clusters. These results should be considered as signatures of thermoreversible associations in the solutions of P2VPPS. To establish a quantitative link between local structure (clusters) and dynamics in dilute solutions of P2VPPS, we combined a thermoreversible gelation theory for the structure of PZ solutions (Li, S.-F.; Muthukumar, M. Theory of Thermoreversible Gelation and Anomalous Concentration Fluctuations in Polyzwitterion Solutions. J. Chem. Phys. 2024, 161, 024903) with a model for the dynamics of the clusters (generalized Zimm model), developed in this work. Using such a theoretical framework, we have predicted the distribution of clusters in the solutions probed with SANS and SAXS. With the distributions, the generalized Zimm model has been used to extract the diffusion constant of the clusters and their characteristic size from the NSE data, where the latter agrees with the values estimated from the SAXS/SANS data. These findings confirm the presence of thermoreversible associations and establish a quantitative link between local structure (clusters) and dynamics in dilute solutions of P2VPPS. Furthermore, with growing interest in technological applications, this work can provide useful insights into the structural and dynamical properties of other PZ solutions.

field theory↗
DOE OSTI2020

Structural Insights into Low and High Recalcitrance Natural Poplar Variants Using Neutron and X-ray Scattering

Here, we used small-angle neutron scattering (SANS) and wide-angle X-ray scattering (WAXS) to study two Populus trichocarpa variants, GW-11012 and BESC-316, with lignin contents of 17.8 and 23.2%, respectively, to understand why the low lignin variant has increased sugar release during liquid hot water (LHW) pretreatment. SANS showed differences in cell wall polymer arrangement in the variants. In GW-11012, the cellulose microfibrils were similar in size to BESC-316 but were not equally spaced and lignin was aggregated rather than homogenously interspersed with other matrix co-polymers. However, after LHW pretreatments, the SANS profiles of the pretreated variants were almost indistinguishable, indicating that the nanoscale structural features could not adequately explain the increased sugar release observed in GW-11012. WAXS analysis revealed higher cellulose crystallinity and larger crystallite size in native and pretreated GW-11012. However, the most significant difference was that the crystallite orientation was approximately 2-fold higher in GW-11012. This suggests that higher crystallite orientation may be favorable for the action of processive cellulases leading to increased sugar release from GW-11012. Our study shows that there is a complex interplay between cell wall polymers during their deposition resulting in changes in lignin distribution and cellulose structure, highlighting the importance of investigating plant cell wall architecture across multiple length scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Variations of Stress Parameters in the Southern California Plate Boundary Around the South Central Transverse Ranges

We examine the stress field in Southern California with a focus on the region near the South Central Transverse Ranges (SCTR), using a refined stress inversion methodology. We independently invert declustered and aftershocks focal mechanisms from the years 1981 to 2017. Comparisons between the stress field orientations and the stress ratios from these inversions provide information on local sources of the stress field. Regionally, the SHmax tends to be toward NNE and the stress ratios vary from transtensional stress regime near the Eastern California Shear Zone (ECSZ), to strike-slip faulting near the SCTR, and toward transpression near the Western Transverse Ranges. Detailed analysis of stress parameters near the SCTR indicates deviations from the regional strike-slip faulting including the following: (1) The San Bernardino Mountain area shows S Hmax direction toward NNW and transpressional stress components likely associated with the motions of the San Andreas Fault and ECSZ; (2) the Cajon Pass and San Gorgonio Pass show transpressional stress regime near the bottom of the seismogenic zone likely associated with the elevated topography; and (3) in Crafton Hills, rotation of the principal stress plunges and SHmax direction and transtensional stress regime below ~10 km, along with lower estimated apparent friction coefficient, suggest a weak fault possibly associated with deep creep. The performed multiscale analysis resolves effects of regional and local loadings. The average stress parameters in the analyzed 37 years do not show significant temporal variations of stress field near the SCTR region.

58 GEOSCIENCES↗
DOE OSTI2021

Exploring the Potential of Using Carbonyl Sulfide to Track the Urban Biosphere Signal

Abstract Cities are implementing additional urban green as a means to capture CO 2 and become more carbon neutral. However, cities are complex systems where anthropogenic and natural components of the CO 2 budget interact with each other, and the ability to measure the efficacy of such measures is still not properly addressed. There is still a high degree of uncertainty in determining the contribution of the vegetation signal, which furthermore confounds the use of CO 2 mole fraction measurements for inferring anthropogenic emissions of CO 2 . Carbonyl sulfide (OCS) is a tracer of photosynthesis which can aid in constraining the biosphere signal. This study explores the potential of using OCS to track the urban biosphere signal. We used the Sulfur Transport and dEposition Model (STEM) to simulate the OCS concentrations and the Carnegie Ames Stanford Approach ecosystem model to simulate global CO 2 fluxes over the Bay Area of San Francisco during March 2015. Two observation towers provided measurements of OCS and CO 2 : The Sutro tower in San Francisco (upwind from the area of study providing background observations), and a tower located at Sandia National Laboratories in Livermore (downwind of the highly urbanized San Francisco region). Our results show that the STEM model works better under stable marine influence, and that the boundary layer height and entrainment are driving the diurnal changes in OCS and CO 2 at the downwind Sandia site. However, the STEM model needs to better represent the transport and boundary layer variability, and improved estimates of gross primary productivity for characterizing the urban biosphere signal are needed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Small-angle scattering interferometry with neutron orbital angular momentum states

Methods to prepare and characterize neutron helical waves carrying orbital angular momentum (OAM) were recently demonstrated at small-angle neutron scattering (SANS) facilities. These methods enable access to the neutron orbital degree of freedom which provides new avenues of exploration in fundamental science experiments as well as in material characterization applications. However, it remains a challenge to recover phase profiles from SANS measurements. We introduce and demonstrate a novel neutron interferometry technique for extracting phase information that is typically lost in SANS measurements. An array of reference beams, with complementary structured phase profiles, are put into a coherent superposition with the array of object beams, thereby manifesting the phase information in the far-field intensity profile. We demonstrate this by resolving petal-structure signatures of helical wave interference for the first time: an implementation of the long-sought recovery of phase information from small-angle scattering measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Advanced characterization of surface-modified nanoparticles and nanofilled antibacterial dental adhesive resins

Nanotechnology can improve the performance of dental polymers. The objective of this study was to modify the surfaces of nanoparticles with silanes and proteins, characterize nanoparticles’ agglomeration levels and interfaces between nanoparticles and the polymeric matrix. Undoped (n-TiO 2 ), nitrogen-doped (N_TiO 2 ) and nitrogen-fluorine co-doped titanium dioxide nanoparticles (NF_TiO 2 ) were synthesized and subjected to surface modification procedures in preparation for Small-Angle X-Ray Scattering (SAXS) and Small-Angle Neutron Scattering (SANS) characterizations. Experimental adhesives were manually synthesized by incorporating 20% (v/v) of n-TiO 2 , N_TiO 2 or NF_TiO 2 (as-synthesized or surface-modified) into OptiBond Solo Plus (OPTB). Specimens (n = 15/group; d = 6.0 mm, t = 0.5 mm) of OPTB and experimental adhesives were characterized using Time-of-Flight Secondary Ion Mass Spectroscopy (ToF-SIMS), 2-D ToF-SIMS chemical imaging and SANS. SAXS results indicated that surface-modified nanoparticles displayed higher scattering intensities in a particle-size dependent manner. ToF-SIMS results demonstrated that nanoparticles’ incorporation did not adversely impact the parental polymer. 2-D ToF-SIMS chemical imaging demonstrated the distribution of Ti + and confirmed nitrogen-doping levels. SANS results confirmed nanoparticles’ functionalization and revealed the interfaces between nanoparticles and the polymer matrix. Metaloxide nanoparticles were successfully fabricated, incorporated and covalently functionalized in a commercial dental adhesive resin, thereby supporting the utilization of nanotechnology in dentistry.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

The effect of low temperature on poly(3-methyl- N -vinylcaprolactam)- b -poly( N -vinylpyrrolidone) diblock copolymer nanovesicles assembled from all-aqueous media

Nanosized polymeric vesicles (polymersomes) self-assembled from double hydrophilic copolymers of poly(3-methyl-N-vinylcaprolactam) n -b-poly(N-vinylpyrrolidone) m (PMVC n -b-PVPON m ) using all aqueous media are a promising platform for biomedical applications, because of their superior stability over liposomes in vivo and high loading capacity. Herein, we explored the temperature-sensitive behavior of PMVC 58 -b-PVPON 65 vesicles using transmission electron microscopy (TEM), dynamic light scattering (DLS), atomic force microscopy (AFM), and small-angle neutron scattering (SANS) in response to lowering the solution temperature from 37 to 25, 20, 14 and 4 °C. The copolymer vesicles with an average size of 350 nm at 37 °C were assembled from the diblock copolymer dissolved in aqueous solution at 4 °C. We show that while the polymersome's size gradually decreases upon the temperature decrease from 37 to 4 °C, the average shell thickness increases from 17 nm to 25 nm, respectively. SANS study revealed that the PMVC 58 -b-PVPON 65 vesicle undergoes a gradual structure evolution from a dense-shell vesicle at 37–25 °C to a highly-hydrated shell vesicle at 20–14 °C to molecular chain aggregates at 4 °C. From SANS contrast matching study, this vesicle behavior is found to be driven by the gradual rehydration of PMVC block at 37–14 °C. The shell hydration at 20–14 °C also correlated with the 4.4-fold decrease in the relative fluorescence intensity from vesicle-encapsulated fluorescent dye, indicating ~80% of the dye release within 12 hours after the vesicle exposure to 14 °C. No significant (<5%) dye release was observed for the vesicle solutions at 37–20 °C, indicating excellent cargo retention inside the vesicles. Our study provides new fundamental insights on temperature-sensitive polymer vesicles and demonstrates that the copolymer assembly into polymersomes can be achieved by decreasing a copolymer aqueous solution temperature below 14 °C followed by solution exposure to ≥20 °C. This type of all-aqueous assembly, instead of nanoprecipitation from organic solvents or solvent exchange, can be highly desirable for encapsulating a wide range of biological molecules, including proteins, peptides, and nucleic acids, into stable polymer vesicles without a need for organic solvents for dissolution of the copolymers that are amphiphilic at physiologically relevant temperatures of 20–37 °C.

36 MATERIALS SCIENCE↗
DOE OSTI2026

An algebraic convolution formulation for multiple-scattering correction in small-angle neutron scattering

Multiple scattering in small-angle neutron scattering (SANS) redistributes spectral weight and distorts structural interpretation, particularly for thick or strongly scattering samples. We develop a finite-dimensional spectral desmearing framework that corrects multiple scattering without resorting to integral transforms or model-dependent extrapolation. The primary intensity is expanded in an orthonormal basis adapted to the isotropic transverse-momentum measure, under which convolution reduces to a recursive tensor contraction, allowing the Poisson-weighted multiple-scattering series to be evaluated directly in a finite-dimensional basis representation. This formulation yields a stable forward–inverse mapping between apparent and primary spectra. Numerical tests demonstrate convergence under repeated convolution and accurate recovery of the single-scattering intensity. Application to SANS measurements collected at multiple neutron facilities, including the Spallation Neutron Source, the High Flux Isotope Reactor, and the Institut Laue-Langevin, shows the quantitative reconstruction of the underlying primary spectrum across a wide range of transmission conditions, including strongly attenuating samples. Here, the method provides a stable, model-agnostic framework for multiple-scattering correction in SANS and enables consistent structural interpretation across instruments and scattering regimes.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗